Higher January 2019 Paper 1 Q16
16
(a) Rationalise the denominator of \(\dfrac{a + \sqrt{4b}}{a - \sqrt{4b}}\) where \(a\) is an integer and \(b\) is a prime number.
Simplify your answer. (3)
Simplify your answer. (3)
(b) Given that \(\left(\sqrt{\dfrac{y}{x}}\right)^{-5} = \dfrac{x^m}{y^m}\) where \(x \ne y\)
find the value of \(m\). (1)
find the value of \(m\). (1)
| Scheme | Marks |
|---|---|
| Eg \(\dfrac{a + \sqrt{4b}}{a - \sqrt{4b}} \times \dfrac{a + \sqrt{4b}}{a + \sqrt{4b}}\) or \(\dfrac{a + 2\sqrt{b}}{a - 2\sqrt{b}} \times \dfrac{a + 2\sqrt{b}}{a + 2\sqrt{b}}\) or \(\dfrac{(a + 2\sqrt{b})^2}{(a + 2\sqrt{b})(a - 2\sqrt{b})}\) | M1 |
| Eg \(\dfrac{(a + \sqrt{4b})(a + \sqrt{4b})}{a^2 - 4b}\) | M1 |
| \(\dfrac{a^2 + 4a\sqrt{b} + 4b}{a^2 - 4b}\) | A1 |
| (3) |
Notes
M1: For multiplying the numerator and denominator by \(a + \sqrt{4b}\) or \(a + 2\sqrt{b}\)
M1: dep on M1 for correctly simplified denominator
A1: for \(\dfrac{a^2 + 4a\sqrt{b} + 4b}{a^2 - 4b}\) or \(\dfrac{(a + 2\sqrt{b})^2}{a^2 - 4b}\)
| Scheme | Marks |
|---|---|
| 2.5 oe | B1 |
| (1) | |
| (4 marks) |